Mean As A Balancing Point Review Mean As A Balancing Point

Mean as the Balancing Point

Mean as the Balancing Point

Mean as the Balancing Point

Mean as the Balancing Point

Review Histograms

Time to get up!!! Scavenger Hunt….

Interquartile Range and Boxplots Module 9 Math 075 Fall 2015

Box and Whisker Diagrams. Anatomy of a Box and Whisker Diagram. Lower Quartile Upper Quartile Lowest Value Median Highest Value Box Whisker 4 5 6 7 8 9 10 11 12 Box Plots

The 5 Number Summary The five number summary consist of : The median ( 2nd quartile) The 1st quartile The 3rd quartile The maximum value in a data set The minimum value in a data set

The 5 Number Summary Step 1 - take the set of numbers given… 34, 18, 100, 27, 54, 52, 93, 59, 61, 87, 68, 85, 78, 82, 91 Place the numbers in order from least to greatest: 18, 27, 34, 52, 54, 59, 61, 68, 78, 82, 85, 87, 91, 93, 100

68 is the median of this data set. The 5 Number Summary Step 2 - Find the median. Remember, the median is the middle value in a data set. 18, 27, 34, 52, 54, 59, 61, 68, 78, 82, 85, 87, 91, 93, 100 68 is the median of this data set.

The 5 Number Summary Step 3 – Find the lower quartile. The lower quartile is the median of the data set to the left of 68. (18, 27, 34, 52, 54, 59, 61,) 68, 78, 82, 85, 87, 91, 93, 100 52 is the lower quartile

The 5 Number Summary Step 4 – Find the upper quartile. The upper quartile is the median of the data set to the right of 68. 18, 27, 34, 52, 54, 59, 61, 68, (78, 82, 85, 87, 91, 93, 100) 87 is the upper quartile

18 is the minimum and 100 is the maximum. The 5 Number Summary Step 5 – Find the maximum and minimum values in the set. The maximum is the greatest value in the data set. The minimum is the least value in the data set. 18, 27, 34, 52, 54, 59, 61, 68, 78, 82, 85, 87, 91, 93, 100 18 is the minimum and 100 is the maximum.

The 5 Number Summary Step 5 – Find the inter-quartile range (IQR). The inter-quartile (IQR) range is the difference between the upper and lower quartiles. Upper Quartile = 87 Lower Quartile = 52 87 – 52 = 35 35 = IQR Looking at the middle 50% of the data

The 5 Number Summary Organize the 5 number summary Median – 68 Lower Quartile – 52 Upper Quartile – 87 Max – 100 Min – 18

Variability about the median Quartiles: Divides the data into four equal parts. (25% of the data will be in each quartile) Some quartiles have more variability than others. We find the Interquartile range: Q3 – Q1

What about outliers? Boxplots are the only graphical representation where we specifically define an outlier Potential outliers are values that are more than 1.5 IQRs from Q1 or Q3 IQR x 1.5; add that product to Q3; any value(s) beyond that point is an outlier to the right Q1; any value(s) beyond that point is an outlier to the left Let’s Practice

Siblings data... Using Stat Crunch, calculate descriptive statistics Let’s calculate (by hand) to see if we have any outliers Q3 – Q1 = IQR IQR x 1.5; add this product to Q3; are there any values in our data set beyond this point to the right? IQR x 1.5; subtract product from Q1; are there any values in our data set beyond this point to the left? Now use Stat Crunch to create a boxplot; are our calculations confirmed with our boxplot?

Graphing The Data Notice, the Box includes the lower quartile, median, and upper quartile. The Whiskers extend from the Box to the max and min.

You should include the following in your interpretation: Range or spread of the data and what it means to your graph Quartiles—compare them. What are they telling you about the data? Median- this is an important part of the graph, and should be an important part of the interpretation. Percentages should be used to interpret the data, where relevant.

Analyzing The Graph The data values found inside the box represent the middle half ( 50%) of the data. The line segment inside the box represents the median

Your turn... In pairs (2 students in a group) , choose a set of data from the Math 075 spreadsheet that is skewed (to left or right); you probably won’t know if the data is skewed until you copy and paste into Stat Crunch and create a graph Create a box plot; put your names on it Label (on the graph) the 5-number summary (with arrows pointing to each value on the graph) Analyze through SOCS (which measure of central tendency should you use? Which measure of spread should you use?); be sure you show your work to justify that a point/points are outliers Now, using the same data, create a histogram. What characteristics of the data does the histogram show that the box plot does not?